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Making any integer with four 2s
There's a cute math puzzle that can be interesting to folks on very different levels: Given exactly four instances of the digit 2 and some target natural number, use any mathematical operations to generate the target number with these 2s, using no other digits. Some examples can be done by elementary school kids: In middle school, kids learn about exponents, factorials, etc.
See this thread for some fun concoctions using integrals, repeating fractions and combinatorial operators. Note that the entity n doesn't actually appear anywhere - it's just a helper to count the number of repeated square roots. I've read about this story in Graham Farmelo's book The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius.
Or read this on Hacker News